CORES AND LARGE CORES WHEN POPULATION VARIES

In a TU cooperative game with population N, a monotonic core allocation allocates each surplus v (S) among the agents of coalition S in such a way that agent i's share never decreases when the coalition to which he belongs expands. We investigate the property of largeness (Sharkey [1982]) for monotonic cores. We show the following result. Given a convex TU game and an upper bound on each agent' share in each coalition containing him, if the upper bound depends only upon the size of the coalition and varies monotonically as the size increases, then there exists a monotonic core allocation meeting this system of upper bounds. We apply this result to the provision of a public good problem. © 1990 Physica-Verlag.